Important Terms & Definitions

Preimage: the figure prior to the transformation.

Image: The figure after the transformation.

Isometry: a transformation that preserves congruence. In other words, a transformation in which the image and preimage have the same side lengths and angle measurements. The following transformations maintain their mathematical congruence.

Translations (a translation is considered a 'direct isometry' because it not only maintains congruence, but it also, unlike reflections and rotations, preserves its orientation.